Nonideal flow distribution

Lipscomb, G.G. Sonalkar, S. Sources of nonideal flow distribution and their effect on the performance of hollow fiber gas separation modules. Separation and Purification Technology 2004, 33 (1), 1-36. 

Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we will develop assume that the residence time distribution function may be attributed to one or the other of these flow situations. The first class of nonideal flow conditions leads to the segregated flow model of reactor performance. This model may be used... 

In general, each form of ideal flow can be characterized exactly mathematically, as can the consequences of its occurrence in a chemical reactor (some of these are explored in Chapter 2). This is in contrast to nonideal flow, a feature which presents one of the major difficulties in assessing the design and performance of actual reactors, particularly in scale-up from small experimental reactors. This assessment, however, may be helped by statistical approaches, such as provided by residence-time distributions. It... 

The characterization of flow by statistical age-distribution functions applies whether the flow is ideal or nonideal. Thus, the discussion in this section applies both in Section 13.4 below for ideal flow, and in Chapter 19 for nonideal flow. 

Figure 13.2 Exit-age distribution function E(t) for arbitrary (nonideal) flow showing significance of area under the E(t) curve...

In this chapter, we consider nonideal flow, as distinct from ideal flow (Chapter 13), of which BMF, PF, and LF are examples. By its nature, nonideal flow cannot be described exactly, but the statistical methods introduced in Chapter 13, particularly for residence time distribution (RTD), provide useful approximations both to characterize the flow and ultimately to help assess the performance of a reactor. We focus on the former here, and defer the latter to Chapter 20. However, even at this stage, it is important to realize that ignorance of the details of nonideal flow and inability to predict accurately its effect on reactor performance are major reasons for having to do physical scale-up (bench —> pilot plant - semi-works -> commercial scale) in the design of a new reactor. This is in contrast to most other types of process equipment. 

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

This chapter deals in large part with the residence time distribution (or RTD) approach to nonideal flow. We show when it may legitimately be used, how to use it, and when it is not applicable what alternatives to turn to. 

The E curve is the distribution needed to account for nonideal flow. 

Conversion in a reactor with nonideal flow can be determined either directly from tracer information or by use of flow models. Let us consider each of these two approaches, both for reactions with rate linear in concentration (the most important example of this case being the first-order reaction) and then for other types of reactions where information in addition to age distributions is needed. 

The study of nonideal flow and liquid holdup can be done by residence time distribution (RTD) experiments (tracing techniques) or by use of correlations derived from literature. Dining this step, physical mechanisms that are sensitive to size are investigated separately from chemical (kinetic or equilibrium) studies (Trambouze, 1990). Here, the fixed bed is... 

A well-known traditional approach adopted in chemical engineering to circumvent the intrinsic difficulties in obtaining the complete velocity distribution map is the characterization of nonideal flow patterns by means of residence time distribution (RTD) experiments where typically the response of apiece of process equipment is measured due to a disturbance of the inlet concentration of a tracer. From the measured response of the system (i.e., the concentration of the tracer measured in the outlet stream of the relevant piece of process equipment) the differential residence time distribution E(t) can be obtained where E(t)dt represents... 

For a continuous reactor with a nonideal flow pattern, characterized by the differential residence time distribution E t), the following expression holds for the conversion nonideai. which is attained in case complete segregation of all fluid elements passing through the reactor can be assumed ... 

Nonideal Flow Patterns 556 Residence Time Distribution 556 Conversion in Segregated and Maximum Mixed... 

A wide range of mass transfer correlations based on Reynold and Graetz numbers have been used to characterize the performance of hollow fiber module contactors. The variation of mass transfer correlations has been attributed to the nonideality in flow distribution, deviation from simple axial flow, and fiber inhomogeneity.Modeling for concentration polarization build-up and two phase flow on the lumen side has also been developed for hollow fiber modules used in filtration.Flow distribution in modules has also been characterized using residence time distribution... 

It will be shown later that it is the exit-age distribution (or the derivative of the F-curve) that is important in determining the efforts of nonideal flow on actual chemical reactor performance. 

As mentioned in Chapters 2 and 4, peak distortion is caused by nonideal equipment not only outside the column but also inside the column. Although sophisticated measurements such as NMR (Tallarek, Bayer, and Guiochon, 1998) allow the investigation of the packed bed only, from a practical viewpoint the observable performance of a column always includes the effects of walls, internal distributors, and filters. Using the method described in this chapter, these are always contained in certain model parameters (e.g., in The column manufacturers have to ensure a proper bed packing and flow distribution (Chapter 4) and, thus, negative influence of imperfections on column performance, for example, on Dax, can be... 

In the present section we indicate how tracer residence time data may be used to predict the conversion levels that will be obtained in reactors with nonideal flow patterns. As indicated earlier, there are two types of limiting processes that can lead to a distribution of residence times within a reactor network. 

The influence of different process and geometrical parameters on conversion was estimated in case of an irreversible first-order catalytic reaction. The influence of temperature nonuniformity (when temperature varies between the channels) had the largest impact on conversion in a nonideal reactor as compared to non-uniform flow distribution and nonequal catalyst amount in the channels. Obtained correlations were used to estimate the influence of a variable channel diameter on the conversion in a microreactor for a heterogeneous first-order reaction. It was found that the conversion in 95% of the microchannels varied between 59 and 99% at = 0.1 and Damkohler number of 2. Figure 9.1a shows conversion as a function of Damkohler number for an ideal microreactor and a microreactor with variations in the channel diameter (aj = 0.1). It can be seen that although the conversion in individual channels can vary considerably, the effect of nonuniformity in channel diameter on the overall reactor conversion is smaller. The lower conversion in channels with a higher flow rate is partly compensated by a higher conversion in channels with a lower flow rate. Due to the nonlinear relation between the channel diameter and the flow rate, the effects do not cancel completely and a decrease in reactor conversion is observed. 

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